Blade Tip Timing Method Research Articles

A recursive calculation method of vibration displacements using blade tip timing in angular domain

Blade tip timing (BTT) is a non-contact measurement technique that can be used to monitor blade vibration in turbomachinery. The raw data measured by BTT is the arrival time of all blades at the same stage. However, most blade vibration monitoring methods based on BTT require the use of blade vibration displacements, which are derived from the raw arrival time data, the blade rotation radius and speed. Conventional BTT methods calculate blade tip displacements by comparing the measured arrival time with the ideal arrival time. The ideal arrival time is obtained by assuming that the rotational speed is constant in a revolution, which is inconsistent with the fact, especially when the rotational speed changes rapidly. In this paper, a recursive calculation method called recursive BTT is proposed to reduce the influence of rotational speed fluctuation on the accuracy of blade tip displacement calculation. Recursive BTT calculates the displacements in the angular domain instead of the time domain. A recursive formula is constructed in the angular domain to calculate the blade vibration displacement by using the angle between the vibrating blades. Compared with the conventional BTT method, which relies on the once-per-revolution (OPR) signal, recursive BTT makes full use of the arrival time of all blades at the same stage to calculate the displacements. The advantage of recursive BTT is illustrated through a simulation, a laboratory test and a full-scale aeroengine test. To evaluate the reliability of the calculated displacements, strain signals are resampled to compare with the calculated displacements in the laboratory test. In the full-scale aeroengine test, due to the lack of strain signals, BTT displacements are used to track the blade natural frequency to qualitatively indicate the influence of displacements on blade vibration monitoring. The results of finite element analysis and modal test are used for verification in the full-scale aeroengine test. Simulation and experimental results demonstrate that compared with existing methods, recursive BTT is robust for calculating blade vibration displacements.

Compressed covariance sensing for blade tip timing measurement

Due to harsh working conditions, rotating blades are prone to failures. Thus, it is urgently needed to monitor blade health. Blade tip timing (BTT) is a promising non-contact vibration technique for rotating blades owing to its high efficiency and long service time. However, due to severe undersampling, traditional spectrum analysis methods are ineffective in identifying characteristic parameters and recovering the power spectrum of vibrations for condition monitoring. To address this issue, this paper proposes a compressed covariance sensing-based BTT (CCS-BTT) method for power spectrum estimation. Specifically, we build a compressed covariance sensing representation model for BTT signal, where the covariance representation can be non-underdetermined owing to the Hermitian Toeplitz structure of the covariance matrix. Then, a universal covariance sampling pattern (UCSP) is derived to ensure the complete covariance information can be efficiently recovered without sparsity constraint. By utilizing the inherent periodicity, the derived UCSP significantly improves the efficiency of BTT measurement. Moreover, for practicality, we present a series of optimized layouts based on UCSP that cover almost all possible cases of probe numbers in BTT measurement. Finally, extensive simulations and experiments validate the effectiveness and performance of CCS-BTT. By shifting the perspective from the signal itself to its covariance, CCS-BTT opens many avenues for the development of BTT signal processing. In addition, the proposed method is expected to be used in deterministic compressive sampling of wide-sense stationary signals.

Advanced Noncontact Sensors for Blade Tip-Timing Systems

The conference paper addresses noncontact sensors for measuring vibrations of machine blades using the Blade Tip Timing method. An overview of sensors based on the electromagnetic principle suitable for the harsh environment of low-pressure stages of steam turbines is presented. Special attention is further given to magnetoresistive sensors and possibilities for increasing their sensitivity. Variants of the sensors with controlled, adaptive, and intelligent operating principles are discussed. The properties and advantages of each version of the solution are demonstrated.

Blade tip timing for multi-mode identification based on the blade vibration velocity

Blade Tip Timing (BTT) is a widely employed non-contact measurement technique for monitoring turbomachinery blade vibrations. The conventional BTT method typically involves computing the expected time of arrival (TOA) and subtracting it from the actual TOA to derive the time difference, subsequently used to calculate blade-tip displacement. However, calculating the expected TOA introduces computational errors. Moreover, obtaining blade-tip vibration displacement under variable rotational speeds necessitates pre-processing to remove trend terms caused by speed fluctuations. To address these challenges, this study introduces a paradigm shift by replacing the traditional displacement-based blade-tip timing (D-BTT) with velocity-based blade-tip timing (V-BTT). Specifically, this approach utilizes the angular information between adjacent sensors and the measured TOA to extract the blade-tip vibration velocity through a Taylor series expansion, thus eliminating the calculating of the expected TOA and improving the computational efficiency. Building upon this methodology, a compressed sensing model for undersampled vibration velocity is established and solved using the Block-OMP algorithm, enabling vibration parameter identification without relying on prior information. By providing a superior representation of mid-frequency components of blade-tip vibration, V-BTT facilitates precise identification of higher-order vibration parameters in multi-mode blade motion. Finally, the efficacy of the proposed method is confirmed through numerical simulations and experiments involving multi-mode blades. The experimental results reveal that the relative errors of the first two modal frequencies for the five blades identified using vibration velocity are all below 0.5%, affirming the method's accuracy. Compared to the traditional D-BTT method, the V-BTT approach reduces the need for trend removal, eliminates calculation errors associated with the expected TOA, and, most importantly, enhances the accuracy of multi-mode frequency identification.

A Single Probe Blade Tip Timing Method for Fast Extraction of Blade Natural Frequency

A Single Probe Blade Tip Timing Method for Fast Extraction of Blade Natural Frequency

Synchronous Vibration Parameter Recognition of Constant-Speed Blades Based on Blade Tip Clearance Measurement

A new method for the synchronous vibration parameter identification of constant-speed rotating blades based on blade tip clearance (BTC) measurement and blade tip timing (BTT) is introduced. A BTC sensor is used to measure the BTC when the blade tip passes through each sensor. The BTT method is used to determine whether the blade tip arrives in advance or lags. The geometric model between the BTC and the blade tip vibration displacement (BTVD) is established, and the BTVD of the blade tip passing through each sensor is obtained. Then, the nonlinear least squares method is used to determine the synchronous vibration parameters of the constant-speed rotating blade. The results show that with an increase in amplitude, the higher the accuracy of the vibration parameter identification proposed in this paper; with a decrease in the random error of the BTC measurement, the higher the accuracy of the vibration parameter identification proposed in this paper; with a decrease in the random error in the measurement of the blade disk dimensions, the higher the accuracy of the vibration parameter identification proposed in this paper. In addition, the smaller the ratio of the blade length to the blade disk radius, the higher the accuracy of the vibration parameter identification method introduced in this paper. Because the structure of the gas turbine compressor and turbine blade disk has a small blade disk ratio, the method proposed in this paper is suitable for the simultaneous vibration parameter identification of gas turbine compressor blades and turbine blades.

A novel OPR-free method for blade tip timing based on adaptive variable reference blades

Monitoring rotor blade vibrations is imperative in aero-engine testing and service. Blade tip timing (BTT), a promising technique for such monitoring, assesses the operational status of rotor blades through non-intrusive measurement of blade tip displacement. Traditional BTT technology relies on the Once-Per-Revolution (OPR) probe, which poses installation challenges and introduces measurement uncertainties in practical applications. This paper introduces a novel OPR-free approach, employing Adaptive Variable Reference Blades (AVRB) for non-intrusive measurement of rotor blade vibrations. The method assumes a stochastic mistuning of blades within the same stage, resulting in non-simultaneous resonance of blades at a given speed. In each revolution, the vibration level of individual blades is determined by assessing the deviation between the average speed of a blade, as measured by two adjacent BTT probes, and the average speed across the entire circumference. Consequently, a non-vibrating blade is adaptively identified and selected as the reference blade. The relative vibration levels among blades vary dynamically during different revolutions, influenced by mistuning features, leading to variability in the reference blades. These adaptive variable reference blades can then replace the OPR probe, aiding in the computation of vibration displacement and further parameter identification of blades. To validate the effectiveness of the proposed method, a five-degree-of-freedom numerical model is utilized for simulation. Additionally, experiments involving both a five-bladed disk and an eight-bladed disk are conducted to validate the proposed approach. Numerical simulations and two sets of test results demonstrate a fundamental agreement between the blade vibration displacement calculated using the proposed method and the outcomes obtained through the traditional BTT method with OPR. The relative error in the identified blade vibration frequency derived from the blade vibration displacement, as determined by both methods, does not exceed 1 %. Additionally, the relative error in the amplitude of the blade vibration displacement is within the range of 10 %.

Prediction of Blade Tip Timing Sensor Waveforms Based on Radial Basis Function Neural Network

As the existing Blade Tip Timing (BTT) vibration measurement methods have serious under-sampling problems, where the blade resonance frequency is usually higher than the sampling frequency of the data acquisition system of the BTT method, resulting in large errors in the identification of blade vibration parameters, new solutions are needed to extend the capability of BTT to nonlinear and multimodal vibration analysis. Therefore, it is the current research direction to pursue new and more accurate measurement and signal processing methods. By analyzing the waveform data from the BTT sensor and using it for vibration analysis, it significantly extends the BTT database. To avoid the current problems of under-sampling and low recognition accuracy, this paper conducts a study on the recognition of rotating blade vibration parameters based on the Radial Basis Function (RBF) model by establishing a RBF neural network prediction model to analyze the static calibration experimental data and predict the waveform of the BTT sensor, and comparing the prediction curves of various models. As the results show, for the RBF model, the prediction accuracy is closely related to the source data of the sampling point data, when the source data predicted by the RBF model is close to the center of the samples, the prediction accuracy is high, meanwhile, the prediction accuracy decreases as it is far away from the center of these data. At the same time, the number of samples is too small to affect the prediction ability of the RBF model. By using this method, more waveforms under the Blade Tip Clearance (BTC) can be predicted with the available sample point data, and the errors in the experimental measurement process can be corrected.

Vibration Parameters Identification of Rotating Blades Based on Blade Tip-Timing Sensor Waveforms

Blade tip-timing is one of the most widely used non-contact measurement methods for rotating blade vibration. The classic blade tip-timing method is to identify the vibration parameters of the blade based on the time of blade tip arrival to the tip-timing sensor installed on the casing. Since the vibration measurement of blade tip-timing is a serious under-sampling method, the blade resonance frequency is usually higher than the sampling frequency of the BTT data acquisition system, resulting in a large identification error of blade vibration parameters. In view of the above shortcomings, a blade vibration parameters identification method is proposed based on the mapping matching between the static waveform of the sensor and the dynamic waveform of the blade tip-timing. The modulation effects of different vibration displacements, velocities and vibration amplitudes on the tip-timing waveform of the sensor are analyzed. The vibration displacements and velocities of the blade tip passing through the sensor are obtained by the waveform mapping method, and then the vibration parameters of the blade are identified. The influence of the number of blade tip-timing sensors on the identification accuracy of the blade vibration parameters identification algorithm is observed based on the waveform mapping theory. The identification accuracy of waveform mapping method is compared with other methods. The results show that compared with the under-sampled time of arrival (TOA) data of classic BTT applications, the modulation of the sensor waveform output by blade vibration can provide additional data, and the waveform mapping method can not only reduce the number of sensors but also improve the identification accuracy of blade vibration parameters. The waveform mapping method has higher identification accuracy of blade vibration parameters compared with the waveform method in the reference.

Active aliasing technique and risk versus error mechanism in blade tip timing

Rotating blades are functional and weak components with a high failure risk, which affects the working ability and operation safety of turbomachinery. Therefore, it is significant to monitor the blades. Blade tip timing (BTT) is a potential measurement technique for rotating blades’ health monitoring owing to its noncontact and efficiency. However, severe undersampling and excessive probes hinder the application of BTT. Thus, identifying the parameters for blade condition monitoring from severely undersampled BTT signals is a hotspot in current research. In this work, we reviewed and summarized a novel bi-probe-based BTT method proposed in our previous work for frequency identification in the non-resonant region. On this basis, we considered the amplitude identification and mathematically derived the maximum frequency that can be identified (supremum frequency) and the maximum error that can be permissible (error tolerance) by the proposed method, which provided theoretical guidance for selecting appropriate layouts and delay schemes. Finally, we revealed the dialectical relationship between the risk of successful reconstruction and the upper bounding of error termed risk versus error mechanism, which facilitated further error reduction.

Biprobes Blade Tip Timing Method for Frequency Identification Based on Active Aliasing Time-Delay Estimation and Dealiasing

Rotating blades are key turbomachinery components with high failure risk due to harsh working conditions. Thus, monitoring the running state of blades is urgently required. Blade tip timing (BTT) is regarded as a potential technology for blade vibration monitoring owing to its noncontact nature and low cost. However, severe undersampling and strict probe layout hinder the application of BTT. As a result of severe undersampling, aliasing and its suppression are the main research topics in BTT. However, in this article, a biprobes method for BTT based on the utilization of aliasing is proposed to identify the natural frequencies of blades. Active aliasing is used in this method to produce aliasing findings at various equivalent sampling frequencies, and the closed-form robust Chinese remainder theorem is used for dealiasing. Unlike the conventional multirate sampling systems for BTT that use a multiprobe configuration or varied speed, the suggested method utilizes varying delay durations to obtain varying equivalent sample frequencies. Furthermore, to ensure that active aliasing and dealiasing form a closed loop, an included angle coprime layout is proposed. Finally, the robustness and effectiveness of the proposed method are verified through numerical and experimental validation.

Multi-probe linear fitting and time of arrival linear correction method to analyze blade vibration based on blade tip timing without once-per-revolution

Blade vibration monitoring can ensure the safe operation of aero-engine rotor blades. Among the methods of blade vibration monitoring, Blade Tip Timing (BTT) method has attracted more and more attention because of its advantages of non-contact measurement. However, it is difficult to install the Once-Per-Revolution (OPR) probe in the confined space of aero-engine, and the failure and instability of the OPR signal will reduce the reliability of the blade vibration analysis results, which directly affects the accuracy of the blade vibration parameters identification. The Multi-Probe linear fitting and Time of Arrival (ToA) Linear Correction method based on the BTT (MP-LC-BTT) without OPR is proposed to reduce the errors of single probe linear fitting method for blade vibration displacement analysis. The proposed method can also correct the calculation error of blade vibration displacement due to the nonlinear change of rotation speed, which can improve the analysis accuracy of the blade vibration displacement. A new blade vibration model conforming to the actual vibration characteristics is established, and the effectiveness of the proposed method is verified by numerical simulation. Finally, the reliability and accuracy of the MP-LC-BTT method have been verified by the experiments which include two high-speed blade test-benches and an industrial axial fan. This method can be used in the actual aero-engine monitoring instead of the BTT method with OPR.

A novel method to improve the precision of BTT under rapid speed fluctuation conditions

It is ultra-important to evaluate the turbine machine blade dynamic stress under abnormal conditions such as rapid rotating speed fluctuation result from surge, rub and foreign object impact. The blade tip timing (BTT) based non-contact dynamic stress measurement method is the most promising technology to replace rotating blade strain gauge. However, there are great challenges to precisely monitor the blade vibration as the rotating speed rapidly fluctuated. It limits the application of BTT considerably. Here, a novel BTT method is proposed to achieve high-precision blade vibration measurement under rapid speed fluctuation conditions. The influence of speed fluctuation on the theoretical arrival time is investigated based on the relationship between blade theoretical arrival time and installation angle. Further, using of the SG filter greatly reduces the computational complexity. The effectiveness of the method is verified by numerical simulation, academic test rig and large industrial turbo fan. The results indicate that the speed measurement error is not more than 0.6 rpm as the accelerating speed as high as 1200 rpm/s. The blade vibration displacement error caused by the rapid speed change can be less than 10 μm. Comparing with existing BTT methods, the average and standard deviation of the blade vibration measurement error are greatly reduced. The method has great value for the application of the blade health monitor and predictive maintenance in turbomachines.

An improved multiple per revolution-based blade tip timing method and its applications on large-scale compressor blades

Blade Tip Timing (BTT) is one of the most effective technologies for blade vibration measurement of turbomachinery. The blade vibration measurement indicates the operational status of the blades, which is of great significance for blade health management and fault diagnosis. However, the approaches and applications of BTT technologies are still facing enormous challenges. This study, based on the traditional once per revolution (OPR) methods, the measurement error of blade vibration induced by the speed fluctuation per revolution (SFPR) is investigated. Considering the effect of the SFPR, an improved multiple per revolution-based BTT method (MPR) for calculating the blade vibration is proposed. Furthermore, numerical simulation and experimental work of the MPR method are executed. Compared with the results of different technologies, the feasibility and reliability of the MPR method are verified by theoretical analysis and experimental verification. The MPR technology is also applied to blade vibration measurement of a large-scale Centrifugal Compressor and a large-scale Axial-Centrifugal Compressor. The conclusions of applications are well practical.

Blade Vibration Difference-Based Identification of Blade Vibration Parameters: A Novel Blade Tip Timing Method

Blade tip timing (BTT) technology is one of the most effective methods for vibration monitoring and health management of rotating blades. However, in actual applications, more blade vibration information means more BTT probes need to be installed, and the calculation of the expected arrival time (ToA) of the blade means the calculation errors introduced to measurement results. In this present study, the relationship between blade vibration (BV) and blade vibration difference (BVD) is investigated, and it can be concluded that blade vibration difference can estimate blade vibration. Then, a two-probe blade vibration measurement system is built and six sets of blade vibration differences can be obtained. Subsequently, this paper researches the parameters identification method of blade vibration based on the blade vibration difference. In the end, BTT experiments show that the blade vibration difference can be measured by the BTT system with high-accuracy, and blade vibration parameters can be analyzed based on the blade vibration difference. Strain experiments demonstrate that the frequency of blade vibration identified by the BTT method is consistent with the strain measurement results. As compared to prior methods, this work, besides reducing the number of probes, eliminates the calculation error of the expected arrival time and is applied for the blade vibration monitoring of any rotating machinery.

An error correction blade tip-timing method to improve the measured accuracy of blade vibration displacement during unstable rotation speed

Rotor blades, being the key part for power and energy conversion, are essential to the safety of turbomachinery. Monitoring the running state of rotor blades is significantly important to ensure the safety of blade operation. The blade tip-timing (BTT) technology has many advantages of non-intrusive measurement being a popular monitor method. The accuracy of vibration data obtained by BTT method is critical to evaluate the running state of blade. However, the blade vibration displacement obtained by the traditional BTT (T-BTT) method and its extended methods still faces the calculation errors caused by unstable rotation speed. To improve the calculation accuracy of blade vibration displacement and minimize the calculation errors caused by unstable rotation speed, the error correction BTT (EC-BTT) method is proposed. In this method, the calculation errors caused by unstable rotation speed are analyzed, and then the calculation errors are eliminated by the derived formula to obtain more accurate vibration displacement data. The EC-BTT method is proved to be feasible and effective by simulation models and a large-scale industry axial fan. The results indicate that the EC-BTT method can eliminate the calculation errors of vibration displacement caused by sudden change and fluctuating speed. The method also can be used in T-BTT and its extended methods.

Blade fault diagnosis using Mahalanobis distance

The fault diagnosis of a rotating multi-blade system has been conducted using the vibration characteristics of the system. For the fault diagnosis, multi-dimensional features related to the system vibration characteristics were extracted and used for monitoring the system health condition in most of previous studies. Recently, blade tip timing (BTT) method becomes increasingly popular to measure the vibration signals of rotating multi-blade systems. Due to the under-sampling characteristics of the method, relatively low frequency components of the vibration signal can be only collected with the BTT method. In this study, a statistical index called the Mahalanobis distance is defined and employed for the fault diagnosis of a rotating multi-blade system having a crack. The effects of crack existence and signal to noise ratio on the reliability of the proposed method using BTT signals obtained with a simulation model are investigated in this study.

Single-Probe Blade Tip Timing: A Novel Method for Anomaly Identification Based on Frequency Shift

Blades are weak and essential parts of an aeroengine. Monitoring the running state of blades is essential for ensuring the safety of aeroengine operation. Blade tip timing (BTT) is considered a promising technique for operational blade vibration monitoring for turbomachinery; however, it is difficult to analyze the BTT signal because of the inherent undersampled limitation. To overcome this limitation, the minimal sensor layout scheme is restricted to be “three.” Usually, more than five probes are required for good signal revolution. This requirement is an installation restriction that limits the application of BTT; however, for users, the conflict between probe layout optimization and real installation restriction is also a serious problem. Motivated by these issues, a single-probe BTT (SP-BTT) method is proposed; the SP-BTT method could extract the shift between natural frequencies, which could be used as a damage index for blade condition monitoring. To validate the effectiveness of the proposed method, numerical simulations and experimental tests are performed.

Analysis and Calibration of Blade Tip-Timing Vibration Measurement Under Variable Rotating Speeds

Blade tip timing (BTT) vibration measurement is a promising on-line blade monitoring method, but various uncertainties bring great challenge in engineering applications. Most existing works are based on the assumption of constant rotating speeds. However, rotating speed is hardly fixed under variable conditions. In this case, these uncertainties always become more serious. To deal with this problem, this paper proposes to investigate BTT measurement derivations in angular domain, instead of time domain. Firstly, this paper systematically analyzes the effects of variable rotating speed, static angle errors and translational blade motions on the accuracy of BTT vibration measurement. Then the corresponding calibration methods are presented by only using times of arrival (TOAs). In the end, Matlab/Simulink simulations are done to validate the proposed method under linear and quadratic variations of rotating speeds. The results demonstrate that BTT measurement deviation under low rotating speeds is more than those under high rotating speeds and BTT measurement deviation due to static angle errors is independent of rotating speeds. And the proposed TOAs-based calibration method can reduce BTT measurement deviation greatly under variable rotating speeds, compared with traditional methods. BTT measurement deviation due to static angle errors can be calibrated by using low rotating speeds and those due to translational blade motions are difficult to be calibrated under variable rotating speeds. Thus simulation results indicate great potential of the proposed method for practical applications of the BTT method.

An OPR-Free Blade Tip Timing Method for Rotating Blade Condition Monitoring

Blade tip timing (BTT) is a noncontact blade vibration measurement method for rotating blade condition monitoring. However, it is difficult to install a once-per-revolution (OPR) probe due to the internal environment limitation of an engine. To solve this problem, an OPR-free BTT method is proposed in this article. Compared with the existing OPR-free methods that are based on blade displacement, this method is based on blade spacing change (BSC). In addition, a probe layout selection method based on minimum redundancy linear array (MRLA) is introduced to reduce the redundancy of the acquired signal. Simulations are conducted to prove that the proposed probe layout selection method has a stronger signal extraction capability and better robustness. The experiment is conducted to show that BSC is an alternative way for rotating blade condition monitoring and the technical route of this article is feasible.